CAIE A-Level Physics 10 D.C. Circuits

Practise drawing and analysing d.c. circuits, source e.m.f., internal resistance, Kirchhoff networks, potential dividers, potentiometers and sensor outputs.

Exam points

draw and interpret complete d.c. circuit diagrams and use correct component symbols
analyse source e.m.f., terminal p.d. and internal resistance through energy transfer and load behaviour
apply Kirchhoff’s laws and equivalent series/parallel resistance to solve circuit networks
calculate potential-divider outputs and compare p.d.s with potentiometers or null methods
explain sensor-dependent divider outputs using thermistors and LDRs

Covered syllabus points

10.1 Practical circuits 10.2 Kirchhoff’s laws 10.3 Potential dividers

[Maximum number: 1]

Which circuit symbol represents a microphone?

Figure for Question 10. D.C. circuits question 1 — CAIE A-Level Physics AS — Option A

Figure for Question 10. D.C. circuits question 1 — CAIE A-Level Physics AS — Option B

Figure for Question 10. D.C. circuits question 1 — CAIE A-Level Physics AS — Option C

Figure for Question 10. D.C. circuits question 1 — CAIE A-Level Physics AS — Option D

[Maximum number: 9]

(a)

State Kirchhoff's first law.

[ 1 ]

(b)

A cell with internal resistance r is connected to two resistors of resistances $R_{1}$ and $R_{2}$ as shown in Fig. 6.1.

Fig. 6.1

The potential differences (p.d.s) across $R_{1}$ and $R_{2}$ are $V_{1}$ and $V_{2}$ respectively.
The terminal p.d. across the cell is V.
The current in the circuit is I.

Use Kirchhoff's laws to show that the total resistance $R_{\mathrm{T}}$ of the external circuit is given by

R_{\mathrm{T}}=R_{1}+R_{2} .

[ 2 ]

(by Kirchhoff's second law) $V=V_{1}+V_{2}$

B1

so $I R_{\mathrm{T}}=I R_{1}+I R_{2}($ and cancelling I gives $) R_{\mathrm{T}}=R_{1}+R_{2}$

or

$V / I=V_{1} / I+V_{2} / I$ (and substituting R gives) $R_{\mathrm{T}}=R_{1}+R_{2}$

B1

(c)

The electromotive force (e.m.f.) of the cell in Fig. 6.1 is 1.50 V .

The values of $R_{1}$ and $R_{2}$ are $10 \Omega$ and $15 \Omega$ respectively. The terminal p.d. of the cell is 1.35 V .
Calculate the internal resistance r of the cell.

[ 2 ]

current in circuit $=1.35 /(10+15)(=0.054 \mathrm{~A})$

C1

r=(E-V) / I

C1

$\begin{aligned} =(1.5-1.35) / 0.054 =2.8 \Omega \end{aligned}$

A1

or

by potential divider principle $\frac{0.15}{1.35}=\frac{r}{25}$

(C2)

$r=2.8 \Omega$

(A1)

or

$I=1.35 /(10+15)(=0.054 \mathrm{~A})$

(C1)

total resistance $=1.50 / 0.054(=27.8 \Omega)$

r=27.8-25

(C1)

$r=2.8 \Omega$

(A1)

(d)

A resistor of resistance $R_{3}$ is added to the circuit in Fig. 6.1, so that the circuit is as shown in Fig. 6.2.

Fig. 6.2

State and explain the effect, if any, of this change on:

[ 4 ]

(i)

the current in the cell

[ 2 ]

(ii)

the terminal p.d. of the cell.

[ 2 ]

[Maximum number: 6]

(a)

Fig. 5.2 shows a circuit with a battery of electromotive force (e.m.f.) 12.0 V connected to a linear potentiometer AB and two identical filament lamps P and Q .

Fig. 5.2

The battery has negligible internal resistance and the lamps each have the same I-V characteristic shown in Fig. 5.1.

When the slider of the potentiometer is at its midpoint, as shown in Fig. 5.2, the current I in the battery is 1.78 A .

Determine:

[ 4 ]

(i)

the current in lamp P
current = A

[ 1 ]

$I=1.55 \mathrm{~A}$

A1

(ii)

the resistance of the potentiometer between its ends A and B.
resistance = $\Omega$

[ 3 ]

$\begin{gathered} I=1.78-1.55 (=0.23 \mathrm{~A}) \end{gathered}$

C1

$\begin{aligned} R =12.0 / 0.23 =52 \Omega \end{aligned}$

A1

(b)

The slider of the potentiometer in (c) is moved to end A .

State and explain the effect on the brightness of lamps P and Q .
lamp P :
lamp Q:

[ 2 ]

[Maximum number: 2]

A student uses a circuit containing an ammeter, a voltmeter and a cell to take measurements to determine the resistance of a length of nichrome wire.

Draw a circuit diagram to show how the components should be connected. Use the symbol for a resistor to represent the nichrome wire.

All question bank results loaded

Covered syllabus points

10. D.C. circuits question 1

10. D.C. circuits question 2

Question (a)

Question (b)

Question (c)

Question (d)

Question (i)

Question (ii)

10. D.C. circuits question 3

Question (a)

Question (i)

Question (ii)

Question (b)

10. D.C. circuits question 4